Automatic Deformable MR-Ultrasound Registration for Image-Guided...

26 Nov 2014 – IGI Journal Club

Automatic Deformable MR-Ultrasound Registration

for Image-Guided Neurosurgery

By H. Rivaz, S. Chen and D. L. Collins in TMI 2013

Presented by: Rachel Sparks


Outline

1. Motivation for MRI-US

2. RaPTOR

a) Correlation Ratio (CR)

b) CR Extension to Patches

c) Outlier Suppression

3. Experimental Design & Results

4. Concluding Remarks


Clinical Motivation:

• Improved patient outcome with

complete tumor removal

Poor visibility of tumor boundary

Tumor proximity to critical brain

structures (vessels, eloquent

regions)

• Pre-operative MRI planning:

Location of the tumor boundary

Location of critical structures

• How to provide intra-operative

feedback and?


Intraoperative imaging approaches

• Intraoperative MRI

High quality, visually similar to pre-operative MRI

Expensive, disruptive to surgery

• Intraoperative video/LRS

Restricted to the superficial surfaces

Cheap, non-disruptive

• Intraoperative US

Intensity inhomogeneity (i.e. signal attenuation, shadowing)

Difficult to interpret (speckle, low-resolution, limited FOV)

Provides minimally disruptive volumetric information



Previous Work MRI-US Fusion

• Surface-based registration (Reinertsen 2007):

Segment structures of interest (vessels) on both modalities

Register surfaces (FEM, ICP)

• Pseduo-US registration (Arbel 2004, Mercier 2012) :

From MRI general pseudo-US

Register pseudo-US to US (ANIMAL, block matching)

• Multimodal image registration

LMI (Klein 2007), Self-Similarity (Rivaz 2012), CR (Roche 1998)

Feature extraction and matching (Penney 2004, Coupé 2012)


Novel Contributions

• Robust Patch-based Correlation Ratio (RaPTOR)- a local

correlation ratio metric

• Derive an analytic derivative for efficient optimization

• Perform outlier rejection to improve robustness of RaPTOR


General Registration Formulation

• Transformation(𝑇) that minimizes dissimilarity metric (𝐷) and

regularization constraint (𝑅)

• In this work 𝑇 is modelled as a Free-form Deformation (FFD)

• Novelty is RaPTOR as choice of 𝐷

𝑇 = min𝑇𝐷 𝐼𝑓 𝑥 , 𝐼𝑚 𝑇 𝜙, 𝑥 + 𝑅 𝑇𝑇 = min

𝑇𝐷 𝐼𝑓 𝑥 , 𝐼𝑚 𝑇 𝜙, 𝑥 +

𝜔𝑅2𝑡𝑟𝑎𝑐𝑒 𝛻𝑇𝑇𝛻𝑇


Correlation Ratio (CR)

• 𝑋, 𝑌 pixel intensities in 𝐼𝑓 and 𝐼𝑚 (choice of correspondence)

CR provides a value of what information in 𝑌 is explained by 𝑋

Define E 𝑌|𝑋 as expected value of 𝑌 given 𝑋*

• CR is calculated as,

𝜂 𝑌 𝑋 =Var[E 𝑌|𝑋 ]

Var[𝑌]

*Different techniques to estimate E 𝑌|𝑋

= 1 −Var[𝑌 − E 𝑌|𝑋 ]

Var[𝑌]


Estimating E 𝑌|𝑋

• A non-parametric approach chosen – flexible, does not assume

specific intensity relationships

• Bin 𝑋 values to estimate 𝑌 value (Parzen windowing)

𝑋 𝑌



• Binning allows closed form solution of 𝜂 𝑌 𝑋 ,

1 − 𝜂 𝑌 𝑋 =1

𝑁 𝜎2

𝑖=1

𝑁

𝑦𝑖2 −

𝑗=1

𝑁𝑏

𝑁𝑗𝜇𝑗

• 𝜎2 variance of 𝑌




1 − 𝜂 𝑌 𝑋 =1

𝑁 𝜎2

𝑖=1

𝑁

𝑦𝑖2 −

𝑗=1

𝑁𝑏

𝑁𝑗𝜇𝑗

• average of 𝑌




1 − 𝜂 𝑌 𝑋 =1

𝑁 𝜎2

𝑖=1

𝑁

𝑦𝑖2 −

𝑗=1

𝑁𝑏

𝑁𝑗𝜇𝑗

• estimated average of 𝑌 according to 𝑋 values (binning)


Patch-based Correlation Ratio

• CR assumes pixel correlations consistent across the image

• US intensities vary in a spatially dependent manner

• Calculate CR independently for several small patches selected

through out the volume

RaPTOR 𝑋, 𝑌 =1

𝑁𝑝

𝑖=1

𝑁𝑝

(1 − 𝜂 𝑌 𝑋: Ω𝑖)


Optimization of 𝐷

• To allow for efficient optimization (gradient descent) need to

define derivative of 𝐷 (chain rule),

𝜕𝐷

𝜕𝑇=𝜕𝑇

𝜕𝜙⋅𝜕𝐼𝑚𝜕𝑇⋅𝜕𝐷

𝜕𝐼𝑚

•𝜕𝐷

𝜕𝐼𝑚needs to be calculated from the RaPTOR metric


Derivative of 𝐷

• Dependent on if 𝑋 corresponds to 𝐼𝑓 or 𝐼𝑚

• In this work 𝑋 corresponds to 𝐼𝑓 (MRI) so,

𝜕𝐷

𝜕𝐼𝑚=𝜕 1 − 𝜂 𝑌 𝑋

𝜕𝑦𝑖

• Once again using the chain rule

𝜕𝐷

𝜕𝐼𝑚=−𝜕𝜎2

𝜕𝑦𝑖

𝑁 𝜎4 𝑖=1𝑁 𝑦𝑖

2 − 𝑗=1𝑁𝑏 𝑁𝑗𝜇𝑗 +

1

𝑁 𝜎2

𝜕 𝑖=1𝑁 𝑦𝑖

2 − 𝑗=1

𝑁𝑏 𝑁𝑗𝜇𝑗

𝜕𝑦𝑖


Robust Patch-based Correlation Ratio

• Some patches provide a poor estimate of correspondence

• Reject outlier patches to improve robustness of CR

• CR is a poor outlier detector

CR varies according to image alignment

Low CR could be misalignment (important to include) or mismatched

patch (outlier to ignore)

• Novel outlier detection according to CR gradient



• CR descent gradient (how image transformation is updated)

should be consistent between neighbouring pixels



• CR descent gradient (how image transformation is updated)

should be consistent between neighbouring pixels



• Formal the gradient descent direction is,𝛻𝐷

𝛻𝑇=𝛻𝐼𝑚𝛻𝑇⋅𝛻𝐷

𝛻𝐼𝑚• This is converted in to a unitless metric

𝑟 = minVar𝜕𝐷𝜕𝑇𝑥

𝜕𝐷𝜕𝑇𝑥

2 ,Var𝜕𝐷𝜕𝑇𝑌

𝜕𝐷𝜕𝑇𝑌

2 ,Var𝜕𝐷𝜕𝑇𝑧

𝜕𝐷𝜕𝑇𝑧

2

• Patches are rejected if 𝑟 is more than a threshold


Evaluation Strategies

1. Synthetic Datasets:

a) CR versus MI values

b) demonstrate outlier rejection

2. Clinical Dataset:

a) Bronze standard: CR versus LMI values

b) Gold standard: landmark correspondences


• Generate random 1D signals with independent noise – ideal MI or

CR value should be zero

• Calculate image metric (MI or CR)

• CR converges faster to ground truth value


Outlier rejection

• Traditional outlier detection determine outliers by value

• CR values highly variable according to image deformation,

location

𝐼𝑓 𝐼𝑚 𝜂 𝑟


Discussion of Synthetic Results

• Demonstrate both MI and CR have the expected results for

random 1D signals

• CR converges to ideal value slightly faster than MI

• CR values hold for a 2D synthetic image


Dataset Description

• 13 patients

• Preoperative MRI

Acquired ~2 weeks prior to surgery

Gd- enhanced T1W

• Post-resection US

2D US with optical tracking (TA003 tracker,

Polaris optical system)

Freehand movement to acquire 200+ slices

3D pixel-based volumetric reconstruction


The following parameters tuned using 1 patient dataset

Parameter Effects Best Value

Patch size Locality versus accuracy 73 (343 voxels)

Patch number Accuracy versus computation time

1000

Hierarchical levels Deformation versus smoothness

2

Spacing between B-Spline nodes

Deformation complexity 20 mm


LMI versus CR

• Selected 1 dataset with a low TME (2.2mm)

• Translated image and calculated LMI, CR

• (0,0) is expected minimum

Making a lot of assumptions (no large deformation, no misalignment)

LMI CR


Qualitative Assessment of Outlier Detection


Registration Evaluation

• Expert selected landmarks

Anatomic Structures (sulci bifurcations, vessels, etc)

6/13 cases had landmarks selected twice (1 month apart)




Discussion

• Outlier rejection to ignore

shadow/resected regions

• Comparison to LMI and RaPTOR very

limited

• CR registration driven by matching

strong edges

Matching tumor/resection margin

Difficult to assess if resection misses

tumor edge


Concluding Remarks

• RaPTOR generally improves MRI-US alignment (2.9 from initial

alignment of 5.9)

• RaPTOR is very quick (30 seconds to register)

• Strong edges drive registration (especially tumor

boundary/resection margin)

• Limited comparisons with other methods (synthetic calculations)

• Dataset available online (BITE Dataset)

Date post:	25-Aug-2020
Category:	Documents
Upload:	others
View:	1 times
Download:	0 times

Automatic Deformable MR-Ultrasound Registration for Image-Guided...

Documents